Thunderbird search index gets corrupt from time to time, and here's a short guide how to make it work again.
I was able to search for things and got some results, but I was unable to open them when clicking on the results. Instead, Thunderbird opened an empty window.
How to fix it in Windows 7 and Vista:
1. Close Thunderbird
2. Open Windows Explorer and go to C:\Users\YOUR_USERNAME\AppData\Roaming\Thunderbird\Profiles\SOMETHING.default, where YOUR_USERNAME is your windows username and SOMETHING is the random profile ID that Thunderbird has created for you.
3. Delete the file global-messages-db.sqlite
4. Start Thunderbird and go to Tools -> Activity Manager. You can see Thunderbird rebuilding the search index. This can take a very long time!
Now you can enjoy the working search, as least as long as it lasts!
If you use another OS, the global-messages-db.sqlite might be in a different location. Here's a guide how to locate your Thunderbird profile folder.